IAI SA7 cheat sheet

Expenditure identity: nominal GDP Y = C + I + G + (X − M); real GDP is computed at constant base-year prices, so only real changes measure growth in output volume rather than price inflation.

Fisher equation: (1 + i) = (1 + r)(1 + π), giving r = (1 + i)/(1 + π) − 1; for low rates the approximation r ≈ i − π is used.

Output gap (%) = (actual − potential)/potential × 100; a positive gap signals capacity pressure and building inflation, a negative gap signals slack and disinflationary pressure.

Short-run Phillips curve trades inflation against unemployment; the long-run curve is vertical at the NAIRU, so monetary policy cannot hold unemployment permanently below it.

Closed-economy multiplier = 1/(1 − MPC); with proportional tax rate t and import propensity m it becomes 1/(1 − MPC(1 − t) + m).

Quantity theory MV = PY: sustained money growth in excess of real output growth shows up as inflation rather than output growth in the long run.

Monetary transmission lags from a policy-rate change to peak inflation effect are commonly 12–24 months; fiscal multipliers typically peak within about 4–8 quarters of the spend.

Recession convention in many jurisdictions: two consecutive quarters of negative real GDP growth; phase sequence is expansion, peak, contraction, trough, recovery.

Leading indicators (inverted yield curve, PMI, new orders, building permits) turn before activity; lagging indicators (unemployment, CPI, inventories) confirm the turn afterwards.

Point elasticity E = (dQ/dP)(P/Q); |E| > 1 elastic so a price cut raises revenue, |E| < 1 inelastic so a price rise raises revenue, |E| = 1 revenue-maximising.

Lerner index L = (P − MC)/P = 1/|E| in equilibrium; L = 0 under perfect competition and rises toward 1 as market power increases.

HHI = Σ s_i² using market shares in percent, range 0–10,000; below 1,500 unconcentrated, 1,500–2,500 moderately concentrated, above 2,500 highly concentrated (US merger guidelines).

Perfect competition long-run equilibrium: P = MC = minimum ATC with zero economic profit; monopoly equilibrium: MR = MC with P > MC and a deadweight loss triangle.

Profit maximisation in any structure: set MR = MC; since MR = P(1 − 1/|E|), the optimal markup is determined solely by the elasticity faced.

Third-degree price discrimination raises profit when sub-markets have materially different elasticities and can be separated; resale between them must be impossible.

Cournot competition with n identical firms gives each a margin (P − MC)/P = 1/(n|E|), converging to the competitive outcome as n grows.

Contestable markets: the threat of hit-and-run entry enforces P = AC even with few incumbents, provided sunk costs are low and incumbents cannot retaliate before exit.

Repeated games: finite repetition of a prisoner's dilemma unravels cooperation by backward induction; indefinite repetition supports tit-for-tat cooperation when discount rates are low.

Standard market failures justifying intervention: market power, externalities, public goods, asymmetric information and missing/incomplete markets; each maps to a distinct instrument.

Negative externality remedy: Pigouvian tax equal to marginal external cost, or a cap-and-trade scheme fixing quantity; a subsidy is the mirror image for positive externalities.

Coase theorem: with defined property rights and zero transaction costs, bargaining reaches efficiency regardless of the initial allocation; real transaction costs justify regulation instead.

Price-cap regulation (RPI − X) caps permitted price increases and rewards cost efficiency; rate-of-return regulation caps profit but invites over-capitalisation (Averch–Johnson effect).

Asymmetric-information remedies: signalling and screening for adverse selection; deductibles, co-insurance, exclusions and monitoring for moral hazard; mandatory pooling where selection is severe.

Taylor rule: i = r* + π + 0.5(π − π*) + 0.5(output gap), where r* is the neutral real rate and π* the inflation target; weights of about one half are typical.

Automatic stabilisers (unemployment benefits, progressive taxes) act without legislative delay; discretionary multipliers are larger at the zero lower bound and smaller in open economies.

Public goods are non-rival and non-excludable, so private markets under-supply them; the free-rider problem calls for public provision, club funding or collective mandates.

Regulatory failure modes to test against any rule: capture, arbitrage, moral hazard from implicit guarantees, and procyclicality of capital or pricing requirements.

Insurance technical price: expected loss cost + expenses + cost of capital × capital allocated + risk/adverse-deviation margin; omitting any element shows up later as reserve or capital strain.

Underwriting cycle: capital inflow → soft market (rates below technical price) → loss shocks deplete capital → hard market → rates rise → capital returns and the cycle repeats.

Capacity constraint: premium volume is bounded by capital × risk-appetite ratio; catastrophe shocks reduce capital, shift the supply of cover left and raise prices.

Duration gap = D_A − (L/A)·D_L; a positive gap means net assets fall when interest rates rise, and immunisation requires D_A = (L/A)·D_L.

Term-structure theories: pure expectations (forward rate = expected future spot), liquidity preference (upward bias for risk), segmented markets and preferred habitat.

Covered interest parity: F/S = (1 + i_d)/(1 + i_f); uncovered parity equates expected depreciation with the interest differential but fails empirically at short horizons.

Relative PPP: expected spot change ≈ domestic inflation − foreign inflation; absolute PPP is a long-run anchor distorted by non-tradables, tariffs and transport costs.

Return period = 1/exceedance probability; a 1-in-200-year loss has 0.5% annual exceedance probability and about a 22% chance of at least one occurrence in 50 years (1 − 0.995^50).

Inverted yield curve: short rates above long rates, historically a leading recession signal reflecting expected policy easing and compressed term premia.

NPV = Σ CF_t/(1 + r)^t − initial outlay; accept positive NPV projects. IRR fails with non-conventional cash flows (multiple roots) and ignores project scale.

Risk-adjusted discount rate = risk-free rate + beta × market risk premium (CAPM); the beta should reflect the project's business risk, not the firm's blended average.

Expected utility: a risk-averse agent has concave utility, so the certainty equivalent lies below the expected monetary value and the gap is the risk premium.

Break-even quantity = fixed costs / contribution per unit; break-even revenue = fixed costs / contribution margin ratio; operating leverage magnifies profit sensitivity to volume.

Principal-agent mitigation: performance-linked pay, deferral and clawback, monitoring, bonding, and aligning the agent's decision horizon with the principal's.

Prospect theory: reference-dependent preferences, loss aversion (losses weighted roughly twice gains), diminishing sensitivity and probability weighting explain framing and status-quo bias.

Real options (defer, expand, contract, abandon, switch inputs) add value over static NPV by preserving managerial flexibility; value rises with uncertainty and time to decide.

Decision analysis: expected monetary value ignores risk preference; decision trees handle sequential choices; sensitivity, scenario and Monte Carlo analysis test robustness to key assumptions.

Cost structures: economies of scale (falling long-run average cost), economies of scope (shared inputs across products), learning curves and network effects producing winner-takes-most outcomes.

Demand for insurance rises with risk aversion, wealth, mandatory purchase requirements and the price of substitutes (self-insurance, captives, derivatives); it falls with premium and retention level.

Supply of cover is capital-constrained: at any time the industry can write only a multiple of available capital, so a capital shock moves the supply curve, not the demand curve.

Price elasticity of insurance demand is low in the short run (cover is often compulsory or contractual) and higher in the long run as buyers redesign programmes.

Asymmetric information costs: adverse selection raises the average risk of the pool, moral hazard raises claim frequency, and both are priced through loadings or managed through contract design.

Comparative advantage and trade: specialisation raises total output, but distributional effects within countries create political pressure for tariffs, quotas and local-content rules.

Globalisation transmission channels: trade linkages, financial market contagion, common monetary conditions and reinsurance capacity all propagate shocks across borders.

Technological change lowers marginal cost of distribution and data processing, shifts market boundaries and increases the returns to scale in underwriting and pricing analytics.

Sustainability and climate economics: physical, transition and liability risks feed into asset values, liability trends and capital requirements, and are increasingly priced rather than treated as externalities.

Return on capital employed = operating profit / capital employed; economic profit (EVA) = invested capital × (ROIC − WACC) and is positive only when returns beat the cost of capital.

WACC = (E/V)·k_e + (D/V)·k_d·(1 − tax rate); k_e from CAPM, and the mix must be rebalanced at market rather than book weights.

Value drivers: growth only creates value if the return on new investment exceeds WACC; growth with returns below WACC destroys value.

Free cash flow = operating cash flow − capital expenditure − change in working capital; discount at WACC for enterprise value and at cost of equity for equity value.

Capital allocation test for an insurer: compare the return on risk-adjusted capital for each line against the hurdle rate and release capital from lines persistently below it.

Merger economics: value accrues from revenue synergies, cost synergies and capital efficiency, offset by the premium paid, integration cost and dis-synergies from culture and systems.

Regulatory capital and rating capital both bind: the effective constraint is the maximum of the two, so optimising only one leaves capital inefficiently deployed.

Pricing for value: technical price must cover expected loss, expenses, cost of capital and a margin for risk; writing below technical price is a transfer of capital to policyholders.

Scenario and stress testing: identify the exposures that could breach risk appetite, size the capital needed, and test management actions for feasibility under the same scenario.